Pandas Profiling Report

Dataset statistics

Number of variables	9
Number of observations	10703
Missing cells	0
Missing cells (%)	0.0%
Duplicate rows	0
Duplicate rows (%)	0.0%
Total size in memory	752.7 KiB
Average record size in memory	72.0 B

Variable types

NUM	9

Warnings

`mean_closeness` is highly correlated with `average_clustering` and 1 other fields	High correlation
`average_clustering` is highly correlated with `mean_closeness` and 1 other fields	High correlation
`assortativity` is highly correlated with `average_clustering` and 1 other fields	High correlation
`rg` has unique values	Unique
`shape` has unique values	Unique

Reproduction

Analysis started	2020-11-25 20:12:01.860857
Analysis finished	2020-11-25 20:12:13.668312
Duration	11.81 seconds
Software version	pandas-profiling v2.9.0
Download configuration	config.yaml

rg
Real number (ℝ_≥0)

UNIQUE

Distinct	10703
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.4006523501
Minimum	0.2647429215
Maximum	0.5000658117
Zeros	0
Zeros (%)	0.0%
Memory size	83.6 KiB

Quantile statistics

Minimum	0.2647429215
5-th percentile	0.314951375
Q1	0.3756062709
median	0.4038566037
Q3	0.4323803498
95-th percentile	0.4666286933
Maximum	0.5000658117
Range	0.2353228901
Interquartile range (IQR)	0.05677407881

Descriptive statistics

Standard deviation	0.04535279828
Coefficient of variation (CV)	0.1131973849
Kurtosis	-0.3184258063
Mean	0.4006523501
Median Absolute Deviation (MAD)	0.02828587499
Skewness	-0.3792377219
Sum	4288.182103
Variance	0.002056876312
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.4469483528	1	< 0.1%
0.4102886314	1	< 0.1%
0.4006058744	1	< 0.1%
0.4185064787	1	< 0.1%
0.409414151	1	< 0.1%
0.3618436218	1	< 0.1%
0.3426848875	1	< 0.1%
0.4506940829	1	< 0.1%
0.392548011	1	< 0.1%
0.4332317889	1	< 0.1%
Other values (10693)	10693	99.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.2647429215	1	< 0.1%
0.2663038185	1	< 0.1%
0.2668979912	1	< 0.1%
0.2674296361	1	< 0.1%
0.2674408081	1	< 0.1%

Value	Count	Frequency (%)
0.5000658117	1	< 0.1%
0.4991441279	1	< 0.1%
0.4991388309	1	< 0.1%
0.4990485847	1	< 0.1%
0.4988778346	1	< 0.1%

mean_displacement
Real number (ℝ_≥0)

Distinct	10648
Distinct (%)	99.5%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	14.38374133
Minimum	0
Maximum	142.2368066
Zeros	56
Zeros (%)	0.5%
Memory size	83.6 KiB

Quantile statistics

Minimum	0
5-th percentile	1.278279263
Q1	6.787500261
median	9.66576856
Q3	20.0354263
95-th percentile	39.12502738
Maximum	142.2368066
Range	142.2368066
Interquartile range (IQR)	13.24792604

Descriptive statistics

Standard deviation	11.59685577
Coefficient of variation (CV)	0.8062475197
Kurtosis	5.940268228
Mean	14.38374133
Median Absolute Deviation (MAD)	3.97054806
Skewness	1.774379636
Sum	153949.1835
Variance	134.4870638
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	56	0.5%
1.134407624	1	< 0.1%
15.12061401	1	< 0.1%
8.208415985	1	< 0.1%
5.978949896	1	< 0.1%
8.077099507	1	< 0.1%
17.82912603	1	< 0.1%
11.10310377	1	< 0.1%
9.250449512	1	< 0.1%
33.07264464	1	< 0.1%
Other values (10638)	10638	99.4%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	56	0.5%
1.016666045	1	< 0.1%
1.023916176	1	< 0.1%
1.035238929	1	< 0.1%
1.035395394	1	< 0.1%

Value	Count	Frequency (%)
142.2368066	1	< 0.1%
119.4764542	1	< 0.1%
117.6691426	1	< 0.1%
115.4518361	1	< 0.1%
105.9717172	1	< 0.1%

shape
Real number (ℝ)

UNIQUE

Distinct	10703
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.003499573175
Minimum	-0.06826915628
Maximum	0.1415545417
Zeros	0
Zeros (%)	0.0%
Memory size	83.6 KiB

Quantile statistics

Minimum	-0.06826915628
5-th percentile	-0.006057928124
Q1	-0.001127639932
median	0.0004272408729
Q3	0.003713336254
95-th percentile	0.02850722117
Maximum	0.1415545417
Range	0.2098236979
Interquartile range (IQR)	0.004840976186

Descriptive statistics

Standard deviation	0.01361309761
Coefficient of variation (CV)	3.889930837
Kurtosis	18.37578008
Mean	0.003499573175
Median Absolute Deviation (MAD)	0.002166574374
Skewness	3.234879993
Sum	37.45593169
Variance	0.0001853164265
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.0001291051405	1	< 0.1%
0.0006601309855	1	< 0.1%
0.000270178324	1	< 0.1%
-0.0001054837404	1	< 0.1%
0.002749565988	1	< 0.1%
-0.002262796314	1	< 0.1%
0.002093124782	1	< 0.1%
0.001835938283	1	< 0.1%
-0.0002375166227	1	< 0.1%
0.01204381302	1	< 0.1%
Other values (10693)	10693	99.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-0.06826915628	1	< 0.1%
-0.06363906968	1	< 0.1%
-0.05755228497	1	< 0.1%
-0.05519934157	1	< 0.1%
-0.05270346023	1	< 0.1%

Value	Count	Frequency (%)
0.1415545417	1	< 0.1%
0.1309540203	1	< 0.1%
0.1248102448	1	< 0.1%
0.1227042489	1	< 0.1%
0.1207423392	1	< 0.1%

density
Real number (ℝ_≥0)

Distinct	7843
Distinct (%)	73.3%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.001448799739
Minimum	0.00134478223
Maximum	0.001676962743
Zeros	0
Zeros (%)	0.0%
Memory size	83.6 KiB

Quantile statistics

Minimum	0.00134478223
5-th percentile	0.001365176148
Q1	0.001407108047
median	0.001453081545
Q3	0.001486241778
95-th percentile	0.001532550889
Maximum	0.001676962743
Range	0.0003321805127
Interquartile range (IQR)	7.913373087e-05

Descriptive statistics

Standard deviation	5.285368923e-05
Coefficient of variation (CV)	0.03648101791
Kurtosis	-0.5889009284
Mean	0.001448799739
Median Absolute Deviation (MAD)	3.784919995e-05
Skewness	0.05820580056
Sum	15.50650361
Variance	2.793512465e-09
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.001359397863	9	0.1%
0.001359883659	7	0.1%
0.00147904071	6	0.1%
0.001379658653	6	0.1%
0.001473681645	6	0.1%
0.001453486232	6	0.1%
0.001357459921	6	0.1%
0.00143358128	6	0.1%
0.001450669599	6	0.1%
0.001365336333	6	0.1%
Other values (7833)	10639	99.4%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.00134478223	1	< 0.1%
0.001346292373	1	< 0.1%
0.001348865727	1	< 0.1%
0.001349015354	1	< 0.1%
0.001349140587	1	< 0.1%

Value	Count	Frequency (%)
0.001676962743	1	< 0.1%
0.001633652961	1	< 0.1%
0.001629685157	1	< 0.1%
0.001628587822	1	< 0.1%
0.001627807059	1	< 0.1%

clique_number
Real number (ℝ_≥0)

Distinct	7
Distinct (%)	0.1%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	4.050920303
Minimum	2
Maximum	8
Zeros	0
Zeros (%)	0.0%
Memory size	83.6 KiB

Quantile statistics

Minimum	2
5-th percentile	3
Q1	3
median	4
Q3	4
95-th percentile	6
Maximum	8
Range	6
Interquartile range (IQR)	1

Descriptive statistics

Standard deviation	0.9969702016
Coefficient of variation (CV)	0.2461095571
Kurtosis	1.581797935
Mean	4.050920303
Median Absolute Deviation (MAD)	0
Skewness	1.258944004
Sum	43357
Variance	0.9939495828
Monotocity	Not monotonic

Histogram with fixed size bins (bins=7)

Value	Count	Frequency (%)
4	5454	51.0%
3	3098	28.9%
5	1056	9.9%
6	696	6.5%
7	371	3.5%
8	23	0.2%
2	5	< 0.1%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
2	5	< 0.1%
3	3098	28.9%
4	5454	51.0%
5	1056	9.9%
6	696	6.5%

Value	Count	Frequency (%)
8	23	0.2%
7	371	3.5%
6	696	6.5%
5	1056	9.9%
4	5454	51.0%

average_clustering
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	9953
Distinct (%)	93.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.1389279499
Minimum	0
Maximum	0.6084742648
Zeros	5
Zeros (%)	< 0.1%
Memory size	83.6 KiB

Quantile statistics

Minimum	0
5-th percentile	0.02934740472
Q1	0.04626148262
median	0.1060590886
Q3	0.147800557
95-th percentile	0.5987907544
Maximum	0.6084742648
Range	0.6084742648
Interquartile range (IQR)	0.1015390743

Descriptive statistics

Standard deviation	0.1558802813
Coefficient of variation (CV)	1.122022468
Kurtosis	3.973982079
Mean	0.1389279499
Median Absolute Deviation (MAD)	0.05666858842
Skewness	2.251427583
Sum	1486.945848
Variance	0.0242986621
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.04879074658	10	0.1%
0.04424778761	10	0.1%
0.04620253165	9	0.1%
0.0443318556	9	0.1%
0.04427577483	8	0.1%
0.04885238998	7	0.1%
0.04430379747	7	0.1%
0.0483396385	7	0.1%
0.0443599493	7	0.1%
0.04586768125	6	0.1%
Other values (9943)	10623	99.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	5	< 0.1%
0.001430615165	1	< 0.1%
0.001432371598	1	< 0.1%
0.001435897436	1	< 0.1%
0.001435897436	1	< 0.1%

Value	Count	Frequency (%)
0.6084742648	1	< 0.1%
0.6081231788	1	< 0.1%
0.6070630498	1	< 0.1%
0.6069814095	1	< 0.1%
0.6067824362	1	< 0.1%

mean_closeness
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	10700
Distinct (%)	> 99.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.0005421201513
Minimum	0.000100637931
Maximum	0.003373289354
Zeros	0
Zeros (%)	0.0%
Memory size	83.6 KiB

Quantile statistics

Minimum	0.000100637931
5-th percentile	0.0001251999322
Q1	0.0001707270123
median	0.0005412433383
Q3	0.000616050486
95-th percentile	0.001927778932
Maximum	0.003373289354
Range	0.003272651422
Interquartile range (IQR)	0.0004453234737

Descriptive statistics

Standard deviation	0.0005235240156
Coefficient of variation (CV)	0.9656973909
Kurtosis	4.430790748
Mean	0.0005421201513
Median Absolute Deviation (MAD)	0.0003022152961
Skewness	2.124331053
Sum	5.802311979
Variance	2.740773949e-07
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.0001025763384	2	< 0.1%
0.0001064349032	2	< 0.1%
0.0001050572457	2	< 0.1%
0.0001209448835	1	< 0.1%
0.0006526277744	1	< 0.1%
0.0001357715662	1	< 0.1%
0.0002696513233	1	< 0.1%
0.0001368234679	1	< 0.1%
0.0002246209363	1	< 0.1%
0.0006164430043	1	< 0.1%
Other values (10690)	10690	99.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.000100637931	1	< 0.1%
0.0001024397823	1	< 0.1%
0.0001025763384	2	< 0.1%
0.00010290546	1	< 0.1%
0.0001029785669	1	< 0.1%

Value	Count	Frequency (%)
0.003373289354	1	< 0.1%
0.003258571217	1	< 0.1%
0.003248603873	1	< 0.1%
0.003212554094	1	< 0.1%
0.00317817879	1	< 0.1%

mean_betweenness
Real number (ℝ_≥0)

Distinct	9627
Distinct (%)	89.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.314002446e-05
Minimum	4.984923249e-09
Maximum	0.00367050182
Zeros	0
Zeros (%)	0.0%
Memory size	83.6 KiB

Quantile statistics

Minimum	4.984923249e-09
5-th percentile	1.481697435e-08
Q1	3.839167337e-08
median	3.803423336e-07
Q3	6.611311975e-07
95-th percentile	0.0002338628676
Maximum	0.00367050182
Range	0.003670496835
Interquartile range (IQR)	6.227395241e-07

Descriptive statistics

Standard deviation	0.0001597285624
Coefficient of variation (CV)	4.819808225
Kurtosis	156.1037236
Mean	3.314002446e-05
Median Absolute Deviation (MAD)	3.355512214e-07
Skewness	10.67970433
Sum	0.3546976818
Variance	2.551321366e-08
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
2.621746929e-08	6	0.1%
1.946777186e-08	6	0.1%
2.05458807e-08	6	0.1%
1.521178447e-08	6	0.1%
1.366464407e-08	6	0.1%
2.363943726e-08	6	0.1%
1.583883465e-08	5	< 0.1%
3.099857352e-08	5	< 0.1%
2.028247514e-08	5	< 0.1%
3.140337018e-08	5	< 0.1%
Other values (9617)	10647	99.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
4.984923249e-09	1	< 0.1%
5.032278139e-09	3	< 0.1%
5.041821018e-09	2	< 0.1%
5.051388041e-09	2	< 0.1%
5.079956941e-09	1	< 0.1%

Value	Count	Frequency (%)
0.00367050182	1	< 0.1%
0.003219041872	1	< 0.1%
0.003209295734	1	< 0.1%
0.002818780816	1	< 0.1%
0.002789564268	1	< 0.1%

assortativity
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	10701
Distinct (%)	> 99.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.8446850952
Minimum	0.4461152309
Maximum	0.9899011033
Zeros	0
Zeros (%)	0.0%
Memory size	83.6 KiB

Quantile statistics

Minimum	0.4461152309
5-th percentile	0.5121904605
Q1	0.8100064214
median	0.8328714993
Q3	0.944246909
95-th percentile	0.9732624376
Maximum	0.9899011033
Range	0.5437858724
Interquartile range (IQR)	0.1342404876

Descriptive statistics

Standard deviation	0.1262026975
Coefficient of variation (CV)	0.1494079844
Kurtosis	1.939443223
Mean	0.8446850952
Median Absolute Deviation (MAD)	0.07910495679
Skewness	-1.51542757
Sum	9040.664574
Variance	0.01592712086
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.9785965306	2	< 0.1%
0.9872670689	2	< 0.1%
0.9454107533	1	< 0.1%
0.9120240158	1	< 0.1%
0.8056972521	1	< 0.1%
0.8151063714	1	< 0.1%
0.8176690268	1	< 0.1%
0.8047817957	1	< 0.1%
0.8337156029	1	< 0.1%
0.8975035897	1	< 0.1%
Other values (10691)	10691	99.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.4461152309	1	< 0.1%
0.4540455353	1	< 0.1%
0.4553403686	1	< 0.1%
0.4588284583	1	< 0.1%
0.4591616346	1	< 0.1%

Value	Count	Frequency (%)
0.9899011033	1	< 0.1%
0.9896933163	1	< 0.1%
0.9896868389	1	< 0.1%
0.9896590498	1	< 0.1%
0.9895339833	1	< 0.1%

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

Count
Matrix

First rows

	rg	mean_displacement	shape	density	clique_number	average_clustering	mean_closeness	mean_betweenness	assortativity
0	0.476249	0.000000	0.001247	0.001360	3	0.001436	0.000139	2.054588e-08	0.892341
1	0.443915	55.140268	0.001491	0.001382	3	0.009798	0.000171	3.911007e-08	0.903483
2	0.429953	50.291421	0.000781	0.001392	3	0.003472	0.000186	7.283252e-08	0.893616
3	0.413413	49.542963	0.002183	0.001388	4	0.008821	0.000172	5.556727e-08	0.924630
4	0.396525	52.880606	-0.000384	0.001404	4	0.015829	0.000202	9.449790e-08	0.902335
5	0.390559	49.946156	-0.001040	0.001398	3	0.015756	0.000192	8.436034e-08	0.905063
6	0.387556	47.897362	-0.001761	0.001391	4	0.019077	0.000176	5.043080e-08	0.915935
7	0.377764	45.165687	-0.003608	0.001410	5	0.019109	0.000201	5.126138e-08	0.923450
8	0.371871	42.052728	-0.005646	0.001406	3	0.025699	0.000201	6.809754e-08	0.898583
9	0.368417	44.360144	-0.006161	0.001396	3	0.024877	0.000183	5.665358e-08	0.923805

Last rows

	rg	mean_displacement	shape	density	clique_number	average_clustering	mean_closeness	mean_betweenness	assortativity
10693	0.384563	6.480627	-0.001703	0.001464	4	0.119147	0.000562	3.589257e-07	0.807784
10694	0.384086	6.376798	-0.001599	0.001459	4	0.121836	0.000557	3.428125e-07	0.817159
10695	0.384200	5.918025	-0.001349	0.001455	4	0.116625	0.000554	3.410380e-07	0.812662
10696	0.383800	5.755412	-0.000956	0.001463	4	0.120885	0.000569	3.477754e-07	0.808373
10697	0.383452	6.059833	-0.000794	0.001461	4	0.125326	0.000561	3.351202e-07	0.810435
10698	0.381531	6.430485	-0.001045	0.001465	4	0.120933	0.000558	3.183952e-07	0.815143
10699	0.382409	5.566823	-0.001161	0.001449	4	0.119005	0.000541	2.914492e-07	0.808140
10700	0.382124	7.064615	-0.001267	0.001464	4	0.130369	0.000566	3.166979e-07	0.813121
10701	0.382152	6.479632	-0.000803	0.001463	4	0.119411	0.000556	3.332482e-07	0.819382
10702	0.381272	6.034650	-0.000905	0.001461	4	0.118066	0.000557	3.243762e-07	0.810699

Overview

Variables

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows